In error detection and correction, majority logic decoding is a method to decode repetition codes, based on the assumption that the largest number of occurrences of a symbol was the transmitted symbol.
In a binary alphabet made of
repetition code is used, then each input bit is mapped to the code word as a string of
-replicated input bits.
The repetition codes can detect up to
transmission errors.
Decoding errors occur when more than these transmission errors occur.
Thus, assuming bit-transmission errors are independent, the probability of error for a repetition code is given by
is the error over the transmission channel.
Assumption: the code word is
This algorithm is a boolean function in its own right, the majority function.